ABCD is a cyclic quadrilateral. The side DC is produced to a point E. If \(\angle BCE=76^\circ\), what is the measure of \(\angle BAD\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 76°
Opposite angles of a cyclic quadrilateral add up to \(180^\circ\). Hence an exterior angle of a cyclic quadrilateral equals the interior opposite angle.
\(\angle BCD=180^\circ-\angle BCE=180^\circ-76^\circ=104^\circ\) (angles on the straight line DCE)
\(\angle BAD=180^\circ-\angle BCD=180^\circ-104^\circ=76^\circ\) (opposite angles of the cyclic quadrilateral)
